General Chemistry Principles, Patterns, and Applications, 2011

The initial concentrations, the changes in concentration that occur as equilibrium is reached, and the final
concentrations can be tabulated.
HCO2H aq
( ) H + ( aq) + HCO2 -( aq)
[HCO2H] [H + ] [HCO2 − ]
initial 0.150 1.00 × 10 −7 0.100
change −x +x +x
final (0.150 − x) x (0.100 + x)
B We substitute the expressions for the final concentrations into the equilibrium constant expression and
make our usual simplifying assumptions, so
Ka = [H +][HCO2-][HCO2H ]
= (x)(0.100 + x)0.150 - x = x(0.100)0.150 = 10 - 3.75 = 1.8 ´10
Rearranging and solving for x,
x = (1.8 ´10 - 4)´ 0.150 M0.100 M = 2.7 ´10 - 4 = [H+]
The value of x is small compared with 0.150 or 0.100 M, so our assumption about the extent of
ionization is justified. Moreover, K aC HA = (1.8 × 10 −4 )(0.150) = 2.7 × 10 −5 , which is greater than
1.0 × 10 −6 , so again, our assumption is justified. The final pH is −log(2.7 × 10 −4 ) = 3.57, compared
with the initial value of 2.29. Thus adding a salt containing the conjugate base of the acid has
increased the pH of the solution, as we expect based on Le Châtelier’s principle; the stress on the
system has been relieved by the consumption of H + ions, driving the equilibrium to the left.
b. C Because HCl is a strong acid, it ionizes completely, and chloride is a spectator ion that can be
neglected. Thus the only relevant acid–base equilibrium is again the dissociation of formic acid, and
initially the concentration of formate is zero. We can construct a table of initial concentrations, changes
in concentration, and final concentrations.
HCO2H aq
( ) H + ( aq) + HCO2 -( aq)
[HCO2H] [H + ] [HCO2 − ]
initial 0.150 0.200 0
change −x +x +x
final (0.150 − x) (0.200 + x) x
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